In this section we use GRAPE to find the time-optimal pulses in the limit \(B=\infty \) . In this limit states with more than one atom in the Rydberg state \(\mathinner {|{r}\rangle }\)  cannot be populated, because the lasers coupling them to states with one atom in the Rydberg state are infinitely far detuned. We start by considering the CZ gate in Sec. REF  and find that the time-optimal global pulse is approximately 10% faster than the pulse of Ref. [1]}. In Sec. REF  we then show that allowing for individual adressability for the atoms brings no speedup for the CZ gate, which is one of the main results of the work. Finally, in Sec. REF  we find the time-optimal global pulse for the three qubit C\(_2\) Z gate, and a second, slightly slower global pulse that also implements a C\(_2\) Z gate. All found pulses are smooth functions of the parameters.
